Abstract

We prove the exponential decay in the case n>2, as time goes to infinity, of regular solutions for the nonlinear beam equation with memory and weak damping utt+Δ2uM(uL2(Ωt)2)Δu+0tg(ts)Δu(s)ds+αut=0 in Q^ in a noncylindrical domain of n+1(n1) under suitable hypothesis on the scalar functions M and g, and where α is a positive constant. We establish existence and uniqueness of regular solutions for any n1.